71.8.2 problem 2

Internal problem ID [14436]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:31:02 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x +y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

dsolve([diff(y(x),x)=y(x)+x,y(0) = 0],y(x), singsol=all)
 

\[ y = {\mathrm e}^{x}-1-x \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 25

DSolve[{D[y[x],x]==y[x]+x,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \int _0^xe^{-K[1]} K[1]dK[1] \]